Genus one cobordisms between torus knots

Peter Feller, JungHwan Park

Published 2019-10-03Version 1

We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\nu^+$ from the Heegaard Floer knot complex and explicit cobordisms constructions. As an application, we determine the induced subgraph of the Gordian graph on the set of vertices that are given by torus knots.